Korepin Festschrift, The: From Statistical Mechanics To Quantum Information Science - A Collection Of Articles Written In Honor Of The 60th Birthday Of Vladimir Korepin

A Collection of Articles Written in Honor of the 60th Birthday of Vladimir Korepin

Leong Chuan Kwek, Simone Severini, Haibin Su

• Publisher: WSPC
• Year: 2013
• eBook ISBN: 9789814460330
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

This volume mainly summarizes the invited talks presented at the 5th Asia-Pacific Workshop on Quantum Information Science (APWQIS) in conjunction with a Festschrift in honor of Professor Vladimir Korepin's 60th birthday. In this Festschrift, we have assembled a medley of interesting articles from some of his friends, well-wishers and collaborators. Comprising both reviews of the state-of-the-art and the latest results, this book covers various aspects of quantum information science, including topics like quantum discord, quantum computing, quantum entanglement, etc.

Contents:

• Cancellation of Ultra-Violet Infinities in One Loop Gravity (V E Korepin)
• Quantum Discord in a Spin System with Symmetry Breaking (B Tomasello, D Rossini, A Hamma and L Amico)
• Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice (S Bose)
• Aspects of the Riemannian Geometry of Quantum Computation (H E Brandt)
• Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian? (T Durt)
• Explicit Formula of the Separability Criterion for Continuous Variables Systems (K Fujikawa)
• Yang–Baxter Equations in Quantum Information (M-L Ge and K Xue)
• Nondistillable Entanglement Guarantees Distillable Entanglement (L Chen and M Hayashi)
• Reduced Density Matrix and Entanglement Entropy of Permutationally Invariant Quantum Many-Body Systems (V Popkov and M Salerno)
• Solitons Experience for Black Hole Production in Ultrarelativistic Particle Collisions (I Ya Aref'eva)
• Sine–Gordon Theory in the Repulsive Regime, Thermodynamic Bethe Ansatz and Minimal Models (H Itoyama)
• On Some Algebraic and Combinatorial Properties of Dunkl Elements (A N Kirillov)
• Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits (M Saniga)
• Monogamy of Entanglement, N -Representability Problems and Ground States (T-C Wei)

Readership: Undergraduate, graduate students and researchers interested in quantum information science, statistical mechanics and mathematical physics.

Chapter 1

CANCELLATION OF ULTRA-VIOLET INFINITIES IN ONE LOOP GRAVITY

V. E. KOREPIN

C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook,

Stony Brook 11794-3840, New York

Quantization of gravity is a formidable challenge for modern theoretical physics. Ultraviolet divergencies are the problem. In 1974 the author used functional integral formalism for the quantization. The background formulation helped to solve the problem in one loop approximation. The author proved that the divergencies cancel on mass shell, because of Einstein’s equations of motion.

Keywords: Gravity, quantization.

1. Introduction

This is a historical note. In 1974 I was an undergraduate student of L. D. Faddeev. I was working on quantum gravity [without matter] in one loop approximation. I discovered [simultaneously with G. t’Hooft M. Veltman] that on mass shell ultraviolet divergences cancel. The text below is a translation of the Diploma.

The diploma was in Russian, it was never published. Recently Faddeev found a reference to my result by an editor in Feynman’s lectures on gravitation¹ (the reference is on page xxxvii of the book). The scan of original diploma can be found in the first line of the webpage.² The result was obtained simultaneously with G. t’Hooft M. Veltman.³ The translation of the diploma follows.^a

The diploma is devoted to quantization of gravity. First appropriate method for quantization of gravity was formulated by Dirac⁷ in 1958 in a frame of Hamiltonian approach. Other methods [essentially equivalent to Dirac’s] were suggested in Refs. 8–13. Hamiltonian approach is not covariant, this makes perturbation theory complicated.

An approach to covariant quantization of gravity was suggested in Refs. 14 and 15, but this method led to violation of unitarity.¹⁶ In the same publication Feynman showed that to restore unitarity of a diagram in a form of a closed ring one has to substract another diagram also in a form of a ring, which describes propagation of fictitious particle. Solution of the problem for any diagram was formulated in 1967 by Fadeev and Popov²⁰ and De-Witt^17–19 [using essentially different approaches]. This approach to quantization contains fictitious...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Preface
• Contents
• Organizing Committee
• List of Speakers
• Photos
• Chapter 1: Cancellation of Ultra-Violet Infinities in One Loop Gravity
• Chapter 2: Quantum Discord in a Spin System with Symmetry Breaking
• Chapter 3: Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice
• Chapter 4: Aspects of the Riemannian Geometry of Quantum Computation
• Chapter 5: Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian?
• Chapter 6: Explicit Formula of the Separability Criterion for Continuous Variables Systems
• Chapter 7: Yang–Baxter Equations in Quantum Information
• Chapter 8: Nondistillable Entanglement Guarantees Distillable Entanglement
• Chapter 9: Reduced Density Matrix and Entanglement Entropy of Permutationally Invariant Quantum Many-Body Systems
• Chapter 10: Solitons Experience for Black Hole Production in Ultrarelativistic Particle Collisions
• Chapter 11: Sine–Gordon Theory in the Repulsive Regime, Thermodynamic Bethe Ansatz and Minimal Models
• Chapter 12: On Some Algebraic and Combinatorial Properties of Dunkl Elements
• Chapter 13: Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits
• Chapter 14: Monogamy of Entanglement, N-Representability Problems and Ground States
• Scientific Programs
• List of Participants